As an alternative to imposing unbiasedness, an estimator's distribution can be centered by requiring that its median be equal to the unknown parameter . If

As an alternative to imposing unbiasedness, an estimator's distribution can be "centered" by requiring that its median be equal to the unknown parameter θ. If it is, ˆ θ is said to be median unbiased. Let Y₁, Y₂, . . . , Y_n be a random sample of size n from the uniform pdf, f_Y(y; θ) = 1/θ, 0 ≤ y ≤ θ. For arbitrary n, is ˆθ = n + 1/n・Y_max median unbiased? Is it median unbiased for any value of n?